If AD=20 and AC=3x+4, Find the value of x then find AC and DC
A figure needs to accompany this question.
Given the median and trapezoid MNOP, what is the value of x?
A. 6
B. 12
C. 8.5
D. 5
E. 7.5
F. Cannot be determined
connot be determined
FIGURE IS PARALEL
To find the value of x, we can equate the lengths of AD and AC.
Given:
AD = 20
AC = 3x + 4
We have:
AD = AC
Substituting the given values, we get:
20 = 3x + 4
Now, let's solve this equation for x:
20 - 4 = 3x
16 = 3x
Divide both sides of the equation by 3:
16/3 = x
Therefore, the value of x is 16/3 or 5.33 (rounded to two decimal places).
Now that we have the value of x, let's find the values of AC and DC:
AC = 3x + 4
AC = 3(5.33) + 4
AC ≈ 15.99 + 4
AC ≈ 19.99 (rounded to two decimal places)
Therefore, AC ≈ 19.99.
DC is the same length as AD, which is given as 20.
Therefore, DC = 20.